Question: Solve for $x$ and $y$ using elimination. ${2x+4y = 56}$ ${2x+5y = 66}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-1$ ${-2x-4y = -56}$ $2x+5y = 66$ Add the top and bottom equations together. ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {2x+4y = 56}\thinspace$ to find $x$ ${2x + 4}{(10)}{= 56}$ $2x+40 = 56$ $2x+40{-40} = 56{-40}$ $2x = 16$ $\dfrac{2x}{{2}} = \dfrac{16}{{2}}$ ${x = 8}$ You can also plug ${y = 10}$ into $\thinspace {2x+5y = 66}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(10)}{= 66}$ ${x = 8}$